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Work has been proceeding to improve the locomotive behavior of kinematic characters under player control. The problem is usually more involved than inverse kinematics with joint constraints etc. Here are few recent machine learning solutions:

Q: What kind of specifications are published that define character locomotion in a given problem space (1) and when is something considered a reference implementation to test against(2)?

See reference implementation for a definition. For example, can ALLSTEPS be considered as a reference for the stepping stone skills? Requirements for GSC-IS Reference Implementations (2003) states that for each level of functionality, a reference implementation should be developed, which is an implementation of the specification to be used as a definitive interpretation. So, running and walking on uneven terrain can be described as the stepping stone problem, which I think is generic for kinematic models with legs. Unwanted behavior is typically defined in the reward weights on the ML model, but I think there is a clear consensus about foot-sliding and temporal incoherence from the motion capture research. See the 2018 paper above and for example Modeling human running on a soccer field and Locomotion-system with irregular IK.

ps: Which non-human figures with joints are popular in demonstrations for player control? You probably know the models in this list which are used to test a given implementation against a, in fluid simulation, ray-casting, 3d printing etc. But demonstrating a stepping stone solution with the Stanford bunny is not ideal.

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